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Problem 1 (10 marks)

An airplane has four engines. On a flight from New York to Paris, each engine has a 0.001 chance of

failing. The plane will crash if at any time two or fewer engines are working properly.

1. a) What is the probability that the plane will crash?
2. b) Given that engine 1 will not fail during the flight, what is the probability that the plane will crash?
3. c) Given that engine 1 will fail during the flight, what is the probability that the plane will not crash?

State clearly your assumptions and show all working.